11.66.* Chapters 12 and 13 show how to incorporate categorical explanatory variables in regression models. This exercise provides a preview. Table 11.25 shows some output for a model for the Houses2 data set at the text website, with y = selling price of home, x1 = size of home, and x2 = whether the house is new (1 = yes, 0 = no).

(a) Report the prediction equation. By setting x2 = 0 and then 1, construct the two separate lines for older and for new homes. Note that the model implies that the slope effect of size on selling price is the same for each.

(b) Since x2 takes only the values 0 and 1, explain why the coefficient of x2 estimates the difference of mean selling prices between new and older homes, controlling for house size.